The best way to get a proper understanding is to write down the truth table completely. You have 3 inputs (A, B, S), so this will give you 2\$^3\$ = 8 combinations: S A B | S' C D | Z --------+---------+-- 0 0 0 | 1 0 0 | 0 0 0 1 | 1 0 0 | 0 0 1 0 | 1 1 0 | 1 0 1 1 | 1 1 0 | 1 1 0 0 | 0 0 0 | 0 1 0 1 | 0 0 1 | 1 1 1 0 | 0 0 0 | 0 1 1 1 | 0 0 1 | 1 It's often useful to add intermediate results to make things more clear. I added a term \$C = (A \land S')\$ and \$D = (B \land S)\$. Now it should be clear that \$Z = (C \lor D)\$.